As one of a D/A conversion apparatus, a D/A conversion apparatus using a noise shaper and a PWM is reported. The D/A conversion apparatus of this method which have been reported hitherto is elucidated by using FIG. 24. Incidentally, this technology is described in "National Technical Report (Volume 34, No. 2, April 1988) pp. 40-45", for example.
FIG. 24 is a block diagram showing an example of a conventional D/A conversion apparatus. Numeral 10 designates a digital filter (DF), and which multiplies a sampling frequency fs of an inputted digital signal by k (k.gtoreq.2). Herein, it is set to k=64. Numeral 11 designates the noise shaper (NS), and word length limitation of the digital signal which is output from the DF 10 is performed, and frequency characteristic of noise is changed to a predetermined characteristic thereby. Herein, it is provided that a noise shaper of third order characteristic is used and an output Y with respect to an input X is represented by an equation (1): EQU Y=X+(1-z.sup.-1).sup.3 .multidot.Vq (1)
where,
Vq: quantizing error, PA1 z.sup.-1 =cos .theta.-j. sin .theta., PA1 j: imaginary number unit. PA1 Vq1: quantizing error. PA1 Vq2: quantizing error. PA1 Vq: quantizing error of quantizer 72, z.sup.-1 =cos .theta.-j.multidot.sin .theta., PA1 j: imaginary number unit.
Moreover, it is provided that the output Y has an output of 11 level (=p). Numeral 19 designates a pulse width modulation circuit (PWM=pulse width modulator), and which converts to a pulse signal of 1-bit having 11 ways of pulse width corresponding to the digital signal output from the NS 11, and outputs as an analog signal. The D/A conversion apparatus of FIG. 24 further converts to the analog signal by using a clock of at least 704 times (=64.times.11) by the PWM 19, after a digital input signal is made to 64 fs of sampling frequency and 11 levels by the DF 10 and the NS 11, and is a D/A conversion apparatus of so called oversampling type for converting the digital signal to an analog signal with a higher sampling frequency.
Further detailed configuration of the NS 11 of FIG. 24 is shown in FIG. 25. Numeral 50 designates a first order .DELTA..SIGMA. modulator (1st order delta-sigma modulator) which outputs by performing quantization of the input X and change of the frequency characteristic of the noise and extracts a quantizing error component -Vq1 and outputs to a next step. An output Y1 with respect to the input X is represented by an equation (2): EQU Y1=X+(1-z.sup.-1).multidot.Vq1 (2)
where,
Moreover, it is here assumed that the output Y1 has outputs (-3-+3) of seven levels (=p1). Numeral 51 designates a second order .DELTA..SIGMA. modulator, and the quantizing error component -Vq1 of the first order .DELTA..SIGMA. modulator 50 and performs quantization of the above-mentioned input -Vq1 and outputs change of the frequency characteristic of the noise. An output Y2 with respect to the input -Vq1 is represented by an equation (3): EQU Y2=Vq1+(1-z.sup.-1).sup.2 .multidot.Vq2 (3),
where,
Moreover, it is here assumed that the output Y2 has outputs (-1, 0, +1) of 3 levels. Numeral 52 designates a differentiator, and the output Y2 is digital-differentiated and is output. An output Y2' with respect to the input Y2 of the differentiator 52 is represented by an equation (4): ##EQU1##
The output Y2' at this time has outputs (-2-+2) of 5 levels (=p2). Numeral 53 designates an adder, and the output Y of the NS 11 is obtained by adding the outputs Y1 and Y2'.
In the D/A conversion apparatus of FIG. 24, result derived by simulation on output signal spectrum in the case of 64 fs of sampling frequency (FS), about 0.02 fs of input signal frequency and 0 dB of the input signal level is shown in FIG. 26. For simplicity, a signal until 0-2 fs is shown here. As mentioned above, although a digital signal of only 11 levels is converted into an analog signal, as shown in FIG. 26, a dynamic range (D.R.) of 120 dB or more is obtained in a signal band of 0-fs/2 by the NS 11.
However, in the configuration shown in FIG. 24, the PWM 19 requires a clock frequency of at least 704 fs. For example, in the case of a sampling frequency fs=48 kHz which is widely used in a digital audio, it becomes extremely high clock frequency such as 704 fs=33.792 MHz, and there is a problem in actual use so that countermeasure to electro-magnetic interference or electro-magnetic disturbance is required.
In the case that the D/A conversion is performed by a method except for the PWM, operation by a clock which is lower than the case of the PWM is possible. For example, a D/A conversion circuit using a resistor array is usable. However, extremely high relative-accuracy is required in the resistor array for this purpose. The reason is that the digital signal which is limited in word length by the NS 11 maintains a high accuracy of 120 dB or more in the original signal band (0-fs/2) in spite of a little word length as mentioned above. Namely, the accuracy of the D/A conversion is decided by the accuracy of the resistor array. And there is such a problem that fabrication of the D/A conversion circuit becomes difficult because the resistor array of the high accuracy is required in order to the D/A conversion of the high accuracy.
By the way, an A/D conversion apparatus of over-sampling type based on a similar concept have been reported. The higherto reported A/D conversion apparatus of this method is elucidated by using FIG. 27. This technology is described in "Institute of Electronics, Information and Communication Engineers Technical Report CS83-198".
FIG. 27 is a block diagram showing an example of the conventional A/D conversion apparatus. Referring to FIG. 27, numeral 70 designates a subtracter which outputs a difference of two analog signals inputted thereto. An analog input from outside is inputted to an addition adding terminal of the subtracter 70. Numeral 71 designates an integrator, and an analog signal output from the subtracter 70 is output by accumulating. Numeral 72 designates a quantizer, and which makes a digital output by converting the analog signal output from the integrator 71 to the digital signal. It is here assumed that quantization of 2 bits (p=4 ways) is performed, and correspondence between input and output is shown in Table 1. Here, it is assumed that the analog input is signals of .+-.1.
TABLE 1 ______________________________________ Input value of Output value of quantizer 72 quantizer 72 ______________________________________ +1.0 . . . +.infin. +1.5 0.0 . . . +1.0 +0.5 -1.0 . . . 0.0 -0.5 -.infin. . . . -1.0 -1.5 ______________________________________
Numeral 79 designates a D/A converter, which converts the output of the quantizer 72 to an analog signal. The output of the D/A converter 79 is inputted to a subtraction terminal of the subtracter 70.
The A/D conversion apparatus of FIG. 27 is known as the A/D converter of a noise shaping type of first order characteristic, and the output Y with respect to the input X is represented by an equation (5): EQU Y=X+(1-z.sup.-1).multidot.Vq (5),
where,
In the A/D conversion apparatus of FIG. 27, result derived by simulation on output signal spectrum in the case of 64 fs of sampling frequency (FS), about 0.02 fs of input signal frequency and 0 dB of input signal level is shown in FIG. 28. For simplicity, a band until 0-2 fs is shown here. As shown in FIG. 28, a dynamic range (D.R.) of about 57 dB is obtained in the signal band of 0-fs/2.
However, in the configuration shown in FIG. 27, it is considered that the D/A converter 79 requires an accuracy of at least the order of the digital signal to be obtained. For example, the case in which the output of the D/A converter 79 has 3% of error as shown in Table 2 is presumed.
TABLE 2 ______________________________________ Input value of D/A Output value of D/A converter 79 converter 79 ______________________________________ +1.5 1.50 +0.5 0.50 -0.5 -0.48 -1.5 -1.50 ______________________________________
Result derivewd by simulation on output signal spectrum in this case is shown in FIG. 29. For simplicity, a band until 0-2 fs is shown here. As shown in FIG. 29, generation of large harmonic distortion is observed, and the dynamic range is seriously deteriorated to about 45 dB in the signal band of 0-fs/2.
This cause is that the output of the D/A converter 79 has nonlinear characteristic. Therefore, in order to obtain a high dynamic range, there is a subject in which a device of high accuracy has to be used for the D/A converter 79.